5 balls are to be placed in 3 boxes. Each box can hold all the 5 balls. In how many ways the balls into the boxes so that no box remains empty, if (a) balls and boxes are all different. (b) balls are identical but boxes are different. (c) balls are different but boxes are identical. (d) balls as well as boxes are identical. (e) balls as well as boxes are identical, but the boxes are kept in a row.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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5 balls are to be placed in 3 boxes. Each box can hold all the 5 balls. In how many ways can we place
the balls into the boxes so that no box remains empty, if
(a) balls and boxes are all different.
(b) balls are identical but boxes are different.
(c) balls are different but boxes are identical.
(d) balls as well as boxes are identical.
(e) balls as well as boxes are identical, but the boxes are kept in a row.
Transcribed Image Text:5 balls are to be placed in 3 boxes. Each box can hold all the 5 balls. In how many ways can we place the balls into the boxes so that no box remains empty, if (a) balls and boxes are all different. (b) balls are identical but boxes are different. (c) balls are different but boxes are identical. (d) balls as well as boxes are identical. (e) balls as well as boxes are identical, but the boxes are kept in a row.
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